1. Express [tex] \frac{sin^2 2 \theta}{1+cos^2 2 \theta} [/tex] as a function of [tex]sin \theta[/tex](adsbygoogle = window.adsbygoogle || []).push({});

here's what I did:

[tex] = \frac{4 sin^2 \theta cos^2 \theta}{1+(2cos^2 \theta -1)^2} [/tex]

[tex] = \frac{4 sin^2 \theta cos^2 \theta}{1+(4cos^4 \theta - 4 cos^2 \theta + 1)} [/tex]

[tex] = \frac{2sin^2 \theta cos^2 \theta}{2cos^2 \theta - 2cos^2 \theta +1} [/tex]

is this correct? can I simplify it more?

2. Write [tex]sin(a+b)sin(a-b)[/tex] as a function of double angles

I used the sum and product formulas to simplify the equation but I did not use the double angle formulas. I'm not quite sure what the question is asking.

Here's what I did:

[tex] = .5 [cos(a+b-a+b)-cos(a+b+a-b)] [/tex]

[tex] = .5 [cos(2b)-cos(2a)] [/tex]

not sure where the double anges come in. any ideas?

3. simplify [tex] \sqrt{2-2cos4 \Theta}[/tex]

i can make it become 1-cos4x but I dont know how to simplify it further because of the cos4. no clue on this one, any help would be appreciated.

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# Homework Help: Trig questions

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